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  • 18-01-2020
  • Physics
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A point moves on the x-axis in such a way that its velocity at time t (t > 0) is given by v=ln t/t . At what value of t does v attain its maximum?

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  • 18-01-2020

Answer:

Explanation:

Given

Velocity of point is given by [tex]v=\frac{\ln t}{t}[/tex]

To get maximum or minimum velocity differentiate v w.r.t t

[tex]\frac{\mathrm{d} v}{\mathrm{d} t}=\frac{\frac{1}{t}\times t-1\times \ln(t)}{t^2}[/tex]

so [tex]1-\ln (t)[/tex] should be equal to zero

[tex]\ln (t)=1[/tex]

[tex]t=e[/tex]

i.e. [tex]t=2.718\ s[/tex]

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